A note on ternary purely exponential diophantine equations

• Autorzy: Yongzhong Hu , Maohua Le
• Języki publikacji: EN

Abstrakty

EN

Let a,b,c be fixed coprime positive integers with min{a,b,c} > 1, and let m = max{a,b,c}. Using the Gel'fond-Baker method, we prove that all positive integer solutions (x,y,z) of the equation $a^x+b^y = c^z$ satisfy max{x,y,z} < 155000(log m)³. Moreover, using that result, we prove that if a,b,c satisfy certain divisibility conditions and m is large enough, then the equation has at most one solution (x,y,z) with min{x,y,z} > 1.

Kategorie tematyczne

• 11D61: Exponential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 171
• Numer: 2
• Strony: 173-182

Daty

wydano

2015

Twórcy

autor

Yongzhong Hu

• Department of Mathematics, Foshan University, 528000 Foshan, Guangdong, P.R. China

autor

Maohua Le

• Institute of Mathematics, Lingnan Normal University, 524048 Zhanjiang, Guangdong, P.R. China

Identyfikatory

DOI

10.4064/aa171-2-4